How many days will it take for 3/4 of a sample of polonium 210 to decay?
To determine the number of days it will take for 3/4 of a sample of polonium-210 to decay, we need to know its half-life. The half-life is the time it takes for half of the original sample to decay.
The half-life of polonium-210 is approximately 138.4 days. This means that every 138.4 days, half of the remaining polonium-210 will decay.
To calculate the number of days it will take for 3/4 of the sample to decay, we can use the formula:
Number of days = Half-life * (log(Initial amount / Remaining amount) / log(2))
In this case, the initial amount is 1, and the remaining amount is 3/4, or 0.75.
Plugging the numbers into the formula, we have:
Number of days = 138.4 * (log(1 / 0.75) / log(2))
Using a scientific calculator or computer software, we can calculate the logarithms and solve for the number of days.
Thus, it will take approximately 193.6 days for 3/4 of the sample of polonium-210 to decay.